# Normal (distribution--specified) quantile regression Distribution--specified quantile regression. An extension of `uninormal` from `VGAM`. It handles effectively `uninormalQlink` via the first linear predictor. ```r uninormalff(link1 = "identitylink", lsd = "loglink", percentile = 50, imethod = 1, isd = NULL, parallel = FALSE, smallno = 1.0e-5, zero = "sd") ``` ## Arguments - `link1`: Link function for the first linear predictor. By default `link1 = "identitylink"`, same as `lmean` from `uninormal`. Set `link1 = "uninormalQlink"` for normal quantile regression. See details below. - `percentile`: Numeric. A vector with the percentiles of interest, between 0 and 100. Used only when `link1 = "uninormalQlink"`. - `lsd, imethod, isd, parallel, smallno, zero`: Same as in `uninormal`, except that `"sd"` is the only accepted value for `zero`. ## Details An extension of `uninormal` adapted to handle `uninormalQlink`, for normal quantile regression (QR) via the first linear predictor. The standard deviation only can be estimated. The second linear predictor is fixed to $\eta_2 = log \sigma$, and `var.arg` is set internally to `FALSE`. Unlike usual QR where the distribution of $Y|X$ is unspecified, `uninormalff()` estimates normal distributions at different quantiles (as entered in `percentile`) of the $Y|X$. For this, set `link1 = uninormaQlink`. To mimic `uninormal` set `link1 = "identitylink"` (default). Initial developments of this work are in **Miranda & Yee (2019)**. See, e.g., `weibullRff`, for another example on distribution specified quantile regression with the two--parameter Weibull distribution. ## Returns An object of class `"vglm"`. See `vglm-class` for full details. ## Note `Q.reg` must be used in the `vglm()` or `vgam()` to enter the response. See example below. This VGAM family function does not handle censored data. ## Author(s) V. Miranda and Thomas W. Yee. ## References Miranda & Yee (2019) **New Link Functions for Distribution--Specific Quantile Regression Based on Vector Generalized Linear and Additive Models**. Journal of Probability and Statistics, Article ID 3493628. Miranda & Yee (2021) **Two--Parameter Link Functions, With Application to Negative Binomial, Weibull and Quantile Regression**. In preparation. ## See Also `uninormalQlink`, `uninormal`, `Q.reg`, `weibullQlink`, `weibullRff`, `CommonVGAMffArguments`. ## Examples ```r ## Not run: x2 <- seq(0,10,length.out = 100) # independent variable sig <- exp(0.5 + 0.15*x2) # non-constant variance b_0 <- 10 # true intercept b_1 <- 0.15 # true slope set.seed(17221) # make the next line reproducible e <- rnorm(100,mean = 0, sd = sig) # normal random error with non-constant variance y <- b_0 + b_1*x2 + e # dependent variable ## Data ndata <- data.frame(y = y, x2 = x2) ## Some percentiles of interest percentile <- c(10, 25, 50, 90) ## Normal quantile regression, zero = NULL fit1 <- vglm(Q.reg(y, length.arg = 4) ~ x2, uninormalff(link1 = "uninormalQlink", percentile = percentile, zero = NULL), data = ndata, trace = TRUE) #summary(fit1) ( my.coef3Q <- coef(fit1, mat = TRUE) ) ## Plots - percentile curves. plot(y ~ x2, pch = 19, ylim = c(-1, 25), main =" Normal quantile regression") abline(h = -3:25, v = 0, col = "gray", lty = "dashed") with(ndata, lines(x2, my.coef3Q[1, 1] + my.coef3Q[2, 1] * x2, col = "red", lty = "dotted", lwd = 4)) with(ndata, lines(x2, my.coef3Q[1, 3] + my.coef3Q[2, 3] * x2, col = "orange", lty = "dotted", lwd = 4)) with(ndata, lines(x2, my.coef3Q[1, 5] + my.coef3Q[2, 5] * x2, col = "blue", lty = "dotted", lwd = 4)) with(ndata, lines(x2, my.coef3Q[1, 7] + my.coef3Q[2, 7] * x2, col = "brown", lty = "dotted", lwd = 4)) legend("topleft", c("90th", "50th", "25th", "10th"), col = c("brown", "blue", "orange", "red"), lty = rep("dotted", 4), lwd = rep(4, 4)) ## Mimicking 'VGAM:uninormal' fit2 <- vglm(y ~ x2, uninormalff(link1 = "identitylink", percentile = NULL, zero = NULL), data = ndata, trace = TRUE) ## End(Not run) ```

uninormalff function